The atmospheric turbulence can cause wavefront distortion when vortex beam carrying orbital angular momentum (OAM) propagates in free space. This brings challenges to the recognition of OAM modes. To realize effective recognition of multichannel vortex beams in atmospheric turbulence, a hybrid interference-convolutional neural network (CNN) scheme is proposed. Here, we compare two different approaches to identify the topological charges under different turbulence levels: the first is based on CNN only and the second is the hybrid scheme of interference and CNN. The simulation shows that the recognition performance of multiple vortex beams under different turbulence levels is improved by our hybrid scheme. Compared with the traditional CNN-based method, the interference-CNN scheme can further identify the sign of topological charge. Moreover, we generalize its feasibility through different kinds of vortex beams with a radial index of p  ≠  0. This provides a versatile tool for large-capacity optical communication based on OAM modes.